A cola-dispensing machine is set to dispense a mean of 2.02 litres into a container labelled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 litres. What is the probability a container will have less than 2 litres?
A) 0.0918
B) 0.3413
C) 0.1926
D) 0.8741

Question

Quizplus · Accepted Answer

We need to find P(X<2) where X is the amount dispensed by the machine. We can standardize the distribution as follows:

Z = (X - μ) / σ = (2 - 2.02) / 0.015 = -1.33

Using a standard normal distribution table, the probability of Z being less than -1.33 is 0.0918. Therefore, the probability of a container having less than 2 litres is 0.0918 or approximately 9.18%.

A Cola-Dispensing Machine Is Set to Dispense a Mean of 2.02